In-silico experiments of needle-shaped particles breakage during shearing have been carried out using DEM simulation. Results of preliminary studies with variation of individual particle strength, compaction ratio, and shearing rate are presented

Grof, Zdenek

Rajniak, Pavol

Stepánek, Frantisek

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Breakage of needle-shaped particles in a combination of compressive and shearing stress field

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II International Conference on Particle-based Methods - Fundamentals and ApplicationsPARTICLES 2011E. Oñate and D.R.J. Owen (Eds)BREAKAGE OF NEEDLE-SHAPED PARTICLES IN ACOMBINATION OF COMPRESSIVE AND SHEARINGSTRESS FIELDZDENĚK GROF∗, FRANTIŠEK ŠTĚPÁNEK∗ AND PAVOL RAJNIAK†∗Department of Chemical Engineering, Institute of Chemical Technology, PragueTechnicka 5, 166 28 Praha 6, Czech Republice-mail: zdenek.grof@vscht.cz, www.vscht.cz/†Merck & Co., Inc., West Point, PA, USAKey words: Granular Materials, DEM, FEM, Contact ProblemsAbstract. In-silico experiments of needle-shaped particles breakage during shearinghave been carried out using DEM simulation. Results of preliminary studies with variationof individual particle strength, compaction ratio, and shearing rate are presented.1 INTRODUCTIONNeedle-shaped crystals are a common occurrence in many pharmaceutical and finechemical processes. Even if the particle size distribution (PSD) obtained in a crystalli-sation step can be controlled, further fluid-solid separation steps such as filtration, filterwashing, drying and subsequent solid handling can often lead to uncontrolled changes inthe PSD due to breakage. Population balance modelling is a common method able to de-scribe PSD changes, however two material- and stress-field specific functions are needed:the breakage kernel (selection function) and the daughter distribution function (break-age function). There are several alternative methodologies for determination of these twofunctions: (i) experimental, (ii) theoretical, or (iii) computational by detailed mechanisticmodelling of the breakage of single particles.Our previous work [1] we have developed a DEM framework for detailed numericalsimulation of needle-shaped crystals movement and breakage. A randomly-packed bed ofelongated particles with a given PSD has been formed by letting the particles to settledown by gravity. The bed of particles has been subjected to uni-axial stress by compress-ing it by two parallel planes. The PSD and all breakage events have been recorded duringthe compression. In a follow-up work [2], results from these computational (in-silico)experiments were used to identify both the breakage kernel and the daughter distributionfunctions.1608Zdeněk Grof, Frantǐsek Štěpánek and Pavol RajniakFigure 1: Scheme of the computational experimentOur current objective is to extend our methodology [1, 2] which has been so far verifiedfor uni-axial compression to more general stress fields.2 METHODOLOGYA methodology based on the discrete element method [3] modified to treat non-sphericalparticles by the multi-element model [4] has been used to simulate the movement andbreakage of individual needle-shaped particles. The magnitude and the location of contactforces at each particle determine the load on the particle. Particles are treated as loadedbeams in order to calculate bending and shear stresses along the particle. When a setthreshold value anywhere along a particle is exceeded the particle breaks into two daughterparticles at the point of maximum stress. A full description of the algorithm has beengiven in our earlier work [1]. Although only normal contact forces among elements ofdifferent particles are considered, the particles are not completely frictionless because oftheirs geometry. They are represented as a compound of overlaid spherical elements,particle roughness is thus caused by gaps between elements. The set-up of computationalexperiment is illustrated in Fig 1.Systems of two sizes have been generated for the simulation of shear induced particlebreakage. Smaller systems containing initially 100 particles composed of 20 discrete el-ements (length = 20) were used for relatively fast simulations aimed to test wide rangeof model parameters. Selected set of parameter values has then been used in simulationswith larger systems of 500, 20-elements long particles. Packing have been generated in thesimulation box by letting particles to settle-down on the flat boundary by the gravitationforce in the z-axis direction. Periodic boundary conditions were imposed in the x- andy-axis directions to avoid the influence of walls. During the next step, another bound-ary wall has been placed above the simulation box and the packing has been graduallycompressed between the two walls. Particles whose loading exceeded a set threshold wereallowed to break. In such a way a group of particle systems of different compression ratiohas been obtained, cf. Fig 2Position of particles near the top and near the bottom of the packing has been frozen.2609Zdeněk Grof, Frantǐsek Štěpánek and Pavol RajniakFigure 2: Illustration of the compression step. Particles are coloured according to their length.The lower layer of particles was then forced to move at a specific velocity in the x-thaxis direction while the top layer was held still. Particles in between then experience ashearing stress in a similar way as material in the ring shear device. Again, the particleswhose loading exceeds a set threshold break into two parts.3 RESULTS AND DISCUSSIONTo find out the effect of the shearing rate on fragmentation of particles in the layer,simulations with different shear rate vs were carried out. The configuration reached afterthe layer moved the length 3.15 times the simulation box width is shown in Fig 3. Startingfrom the same configuration (cf. Fig 2b), lower layer moved at two different speeds. Fromvisual observation it is apparent that more breakage occurred at faster speed (Fig 3a)than at the 50 times slower one (Fig 3b). The breakage takes place mostly in the lowerhalf of the layer in both cases.Particle size distribution and number mean particle size evolution during shearing isshown in Fig 4. Here the larger and smaller systems are compared. One can see thatresults for both systems are comparable suggesting that for the computations one can userelatively low number of particles and smaller computational box. Regarding the velocityeffect, the fragmentation is lower at slower velocities which is consistent with what onewould expect: more careful (slower) particle displacement leaves more time for particlelayer rearrangements and thus there is lower chance of local stress built-up and exceedingparticle mechanical strength. If the shearing rate is much slower then the rate of layerrearrangements, then the shearing is in a pseudo-steady state and fragmentation does notdepend on shearing rate anymore. Even in the pseudo-steady state regime the breakagecan still occur if some particles get jammed during their displacement. As we would liketo restrict ourselves to situations where the dynamical effects can be neglected, we aimto set the shearing velocity so low to be in the pseudo-steady state regime. It can be seenfrom results in Fig 4, that the substantial fragmentation occurs at the largest velocity,while there is less fragmentation and lower dependence on shearing velocity at remainingslower velocities.3610Zdeněk Grof, Frantǐsek Štěpánek and Pavol Rajniaka bFigure 3: Illustration of the shearing step: (a) fast shearing, (b) slow shearing. Initial configuration,cf. Fig 2bThe simulation is stopped when the shearing distance reaches 6.25 and 12.5 timescomputation box width in larger and smaller system, respectively. Based on results, thislength is sufficient as most of fragmentation occur at the beginning and no more or littlefragmentation take place later as all jammed particles broke down and can be freelyshifted.Results investigating the effect of particle strength are introduced in Fig 5. Systemsof three different particle strengths at two different compaction ratios are compared. Itcan be seen that there are small differences between particles of strength 30 and 40 atthe lower compaction (88% of the initial particle height). The size of particles furtherdecreases as expected during shearing. It is interesting to observe that the change ofsize distribution during shearing is smaller for weakest particles (20) than for strongerparticles (40). The explanation is that the weakest particles have already broken moreduring compaction and short particles are less likely to get jammed and break duringshearing.4 CONCLUSIONSA preliminary study has been made to investigate the possibility to use in-silico exper-iments to study breakage of needle-shaped particles under shearing stress. Our objectiveis to use these results in identifying breakage kernels and the daughter distribution func-tions. We have demonstrated that the simulation of shearing induced breakage is feasibleeven for modestly sized systems. There are two regimes in respect to the shearing veloc-ity: The breakage depends on shearing velocity at high velocities. However, breakage isvelocity independent when the shearing velocity is low enough. More simulations will benecessary to identify the transition between these regimes.4611Zdeněk Grof, Frantǐsek Štěpánek and Pavol Rajniak 0 10 20 30 40 50 60 70 80 90 0  2  4  6  8  10  12  14  16  18  20no. of particlessizeinitv100v20v10v2v1a 9 10 11 12 13 14 15 16 17 18 0  50  100  150  200  250number mean sizeshearing distancev100v20v10v2v1b 0 50 100 150 200 250 300 350 400 450 0  2  4  6  8  10  12  14  16  18  20no. of particlessizeinitv100v20v10v2v1c 10 11 12 13 14 15 16 17 18 0  50  100  150  200  250number mean sizeshearing distancev100v20v10v2v1dFigure 4: Effect of shearing velocity: Initial and final particle size distribution at different shearingvelocities. Number average particle length evolution during shearing. Plots a) and b) are for smallersystem, while plots c) and d) are for larger system. Shearing distance is dimensionless, with the unitlength corresponding to the diameter of single element. Shearing velocity is also denoted in dimensionlessunits.5612Zdeněk Grof, Frantǐsek Štěpánek and Pavol Rajniak 0 10 20 30 40 50 60 70 80 90 100 0  2  4  6  8  10  12  14  16  18  20no. of particlessize20 ini30 ini40 ini203040a 13.5 14 14.5 15 15.5 16 16.5 17 17.5 18 18.5 0  50  100  150  200  250number mean sizeshearing distance203040b 0 10 20 30 40 50 60 70 80 0  2  4  6  8  10  12  14  16  18  20no. of particlessize20ini30ini40ini203040c 10.5 11 11.5 12 12.5 13 13.5 14 14.5 15 15.5 0  50  100  150  200  250number mean sizeshearing distance203040dFigure 5: Effect of particle strength: Initial and final particle size distribution with particle strength of20, 30 and 40 kPa. Number average particle length evolution during shearing. Plots a) and b) are forlow compaction ratio (88%). Plots c) and d) are for higher compaction ratio (76%). Shearing distance isdimensionless, with the unit length corresponding to the diameter of single element.6613Zdeněk Grof, Frantǐsek Štěpánek and Pavol RajniakACKNOWLEDGEMENTFunding from Czech Ministry of Education through grant MSM6046137306 is acknowl-edged.REFERENCES[1] Grof, Z., Kohout, M. and Štěpánek, F. Multi-scale simulation of needle-shaped par-ticle breakage under uni-axial compaction. Chem. Eng. Sci. (2007) 62:1418–1429.[2] Grof, Z., Schoellhammer, C.M., Rajniak, P. and Štěpánek, F. Computer and experi-mental investigation of needle-shaped crystal breakage. Int. J. Pharmaceutics (2011)407:12–20.[3] Cundall, P.A. and Strack, O.D.L. A discrete numerical model for granular assemblies.Géotechnique (1979) 29:47–65.[4] Favier, J.F., Abbaspour-Fard, M.H., Kremmer, M. and Raji, A.O. Shape representa-tion of axi-symmetrical, non-spherical particles in discrete element simulation usingmulti-element model particles. Eng. Comput. (1999) 16:467–480.7614

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Breakage of needle-shaped particles in a combination of compressive and shearing stress field

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